1. Technical Field
The present invention relates to the field of processing signals comprised of a mixture of signals from a plurality of sources, and more particularly to processing signals comprised of a mixture of signals from a plurality of sources in the case where the number of signal sources exceeds that of the number of detecting sensors and where the number of signal sources, the individual signals from the signal sources, and the mixing matrix are unknown.
2. Description of the Art
Blind mixed signal separation is a phrase that describes the separation of signals from a plurality of sources when the number of sources, the individual signals from the signal sources, and the mixing matrix are unknown. When the number of sources exceeds the number of sensors used for receiving a mixed signal from the sources, the case is known as the “over-complete” case. In theory, it is possible to perfectly separate mixed signals if the number of signal sources is equal to or less than the number of sensors. However, the separation of mixed signals in the over-complete case is difficult and perfect separation is not possible, even theoretically.
The separation of mixed signals is an issue in many situations, two important examples of which include cellular communications, especially in urban environments, and in spoken dialogue information retrieval on mobile platforms. In cellular communications, the interference signals correspond to the signals that get reflected from various scatterers (multipath) such as buildings and noise. On the other hand, in spoken dialogue-based systems on mobile platforms, the interference signals correspond to other speakers and noise. The signal that is received at a sensor is a mixed signal that includes interference signals as well as the desired signals, together discussed herein as source signals. In these cases, it is not practical to know a priori the number of interfering signals (which are considered as different signal sources), and hence, it is not practical to use the same number of sensors, e.g., antennas in the case of cellular communication and microphones in the case of spoken dialogue-based systems, as that of the signal sources. It is therefore imperative to develop a signal separation system that can handle the over-complete case for efficient and clear cellular communication and for robust spoken dialogue-based information retrieval on mobile platforms. This is important to provide clear communication in the case of cellular phones and to improve speech recognition in the case of spoken dialogue-based information retrieval systems.
As stated, since the number and nature of source signals change, it is not practical to know them a priori. Therefore, it is not always practical to apply signal separation techniques that work well when the number of source signals is equal to the number of sensors. Further, in this case, since how the signals get mixed (e.g., the mixing matrix) is unknown, it is necessary to apply blind techniques for the separation of the source signals.
The solution of the over-complete case is a relatively recent topic within the research community. A few techniques have been developed, as discussed in the references provided at the end of this Background section. These techniques generally suffer from several drawbacks. They suffer from limited signal separation efficiency. Further, they lack robustness for different types of mixing matrices and signals. Additionally, they are computationally sluggish, making real-time implementation difficult. Finally, their theoretical limitations are difficult to ascertain, making them difficult to apply due to uncertainty regarding their performance.
More specifically, in M. Zibulevsky and B. A. Pearlmutter, “Blind source separation by sparse decomposition,” University of New Mexico technical report No. CS99-1, 1999, the estimation of the mixing matrix and source signals takes place separately, which does not allow for efficient separation of the mixed signals, since the estimation of the mixing matrix effects the estimation of the source signals, resulting in complex and expensive computation. In L. Q. Zhang, S. Amari and A. Cichocki, “Natural gradient approach to blind separation of over and under complete mixtures,” Proceedings of ICA'99, Aussois, France 1999, a natural gradient approach to blind source separation of over and under-complete mixtures is described from a theoretical point of view. The method described makes use of Lie group structures in the source signals and uses Reimann metrics. A learning algorithm based on the minimization of mutual information is described. In Te-Won Lee, M. S. Lewicki, M. Girolami and S. J. Sejnowski, “Blind source separation of more sources than mixtures using overcomplete representations,” IEEE Signal processing letters, Vol. 6, No. 4, pp. 87–90, April 1999, another probabilistic approach is described. This technique estimates the mixing matrix and the source signals separately, hence having the same disadvantage as Zibulevsky et al., mentioned above. The mixing matrix is estimated by considering it as basis vectors and an approximated learning rule is applied. In this approximation, it is assumed there is no additive noise and that there exists temporal independence of the samples of the mixtures. The technique in Lee et al., is demonstrated only for use with clean mixed signals and a fixed mixing matrix. In H-C. Wu, J. C. Principe and D. Xu, “Exploring the time-frequency microstructure of speech for blind source separation,”, ICASSP'98, pp. 1145–1148, an approach based on the concept of thinning and estimating the spatial directions of the mixing matrix is applied for blind source separation. This approach is not probabilistic-based, which limits its ability to separate source signals. Furthermore, the approach appears to be effective only when the number of sensors is equal to the number of sources. In P. Bofill and M. Zibulevsky, “Blind separation of more sources than mixtures using sparsity of their short-time fourier transform,” Proc. Of ICA workshop, July 1999, pp. 87–92, a probabilistic approach is described in which the mixing matrix and the source signals are estimated separately, thus suffering from the same disadvantage as Zibulevsky et al., mentioned above. Finally, all of these references suffer from the drawback of an unknown theoretical performance bound. Thus, a user operating a system based on one of these techniques cannot know the theoretical limitations of their system.
It is desirable to provide a system for solving the over-complete case that overcomes these limitations and that estimates the mixing matrix jointly to provide an advantage of efficiently separating the mixed signals by taking into account the effect of estimating the mixing matrix on the estimate of the source signals, and which allows for efficient convergence on a solution.
The following references are provided to assist the reader in gaining more knowledge regarding the state of the art in this technical area.